Philosophy of Mathematics: Structure and Ontology

* Read * Philosophy of Mathematics: Structure and Ontology by Stewart Shapiro ↠ eBook or Kindle ePUB. Philosophy of Mathematics: Structure and Ontology As Benacerraf first noted, we are confronted with the following powerful dilemma. Shapiro concludes by showing how a structuralist approach can be applied to wider philosophical questions such as the nature of an object and the Quinean nature of ontological commitment. Using this framework, realism in mathematics can be preserved without troublesome epistemic consequences. On this view, the subject matter of arithmetic, for example, is not a fixed domain of numbers independent of each other, b

Author

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Stewart Shapiro

Rating

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4.13 (951 Votes)

Asin

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0195094522

Format Type

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paperback

Number of Pages

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296 Pages

Publish Date

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2016-12-13

Language

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English

DESCRIPTION:

As Benacerraf first noted, we are confronted with the following powerful dilemma. Shapiro concludes by showing how a structuralist approach can be applied to wider philosophical questions such as the nature of an "object" and the Quinean nature of ontological commitment. Using this framework, realism in mathematics can be preserved without troublesome epistemic consequences. On this view, the subject matter of arithmetic, for example, is not a fixed domain of numbers independent of each other, but rather is the natural number structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle. As a way out of this dilemma, Shapiro articulates a structuralist approach. Do numbers, sets, and so forth, exist? What do mathematical statements mean? Are they literally true or false, or do they lack truth values altogether? Addressing questions that have attracted lively debate in re

Stewart Shapiro, Professor of Philosophy, Ohio State University at Newark.

"This book is an important contributionpresenting an original, structuralist philosophy and axiomatic framework in comprehensive detail, placing it in broad philosophical and historical perspective, and comparing it systematically with other approaches seen as leading structuralist alternatives to the one set forth by Shapiro himselfis is an interesting, important, and thought-provoking book."--Journal of Symbolic Logic